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Monetary Theory I | © Sanjay K. Chugh 1 Department of Economics Boston College Economics 8861.01 Monetary Theory I Syllabus Professor Sanjay Chugh Fall 2015 Meetings: Tuesdays and Thursdays, 10:30am-11:45am Maloney Hall 313 Email address: [email protected] Prerequisites: The first-year economics Ph.D. sequence (in particular, EC750.01 and 751.01). Auditors and other upper-level students welcome, but are expected to actively participate in both class discussion and assignments. Grading: The final course grade will be based on: 1. Completing a “computational primer:” solving computationally for the deterministic steady state of the basic RBC model – 10% of final grade. 2. Computationally solving and simulating the basic RBC model, tabulating business cycle statistics and impulse responses (written as a complete, short paper) – 20% of final grade. 3. Two other projects to be assigned during the course, each of which will be computationally and/or analytically oriented (each written as a complete, short paper) – (total of 20% of final grade). 4. In-class presentation of a paper (from a designated set of papers) – 20% of final grade. 5. Assorted assignments, short writing pieces, quizzes, etc – 10% of final grade. Reference Texts: Some “all-purpose” macroeconomics and texts that are likely to be useful to have on your shelf/eshelf: 1. Frontiers of Business Cycle Research, 1995. Edited by Thomas F. Cooley. Princeton University Press. 2. Equilibrium Unemployment Theory, 2 nd edition, 2000. By Christopher A. Pissarides. MIT Press. 3. Labor Markets and Business Cycles, 2010. By Robert Shimer. Princeton University Press. 4. Recursive Macroeconomic Theory, 3 nd edition, 2012. By Lars Ljungqvist and Thomas J. Sargent. MIT Press. 5. Recursive Methods in Economic Dynamics, 1989. By Nancy L. Stokey and Robert E. Lucas, Jr., with Edward C. Prescott. Harvard University Press.

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Monetary Theory I | © Sanjay K. Chugh 1

Department of Economics Boston College

Economics 8861.01 Monetary Theory I

Syllabus Professor Sanjay Chugh

Fall 2015 Meetings: Tuesdays and Thursdays, 10:30am-11:45am Maloney Hall 313 Email address: [email protected] Prerequisites: The first-year economics Ph.D. sequence (in particular, EC750.01

and 751.01). Auditors and other upper-level students welcome, but are expected to actively participate in both class discussion and assignments.

Grading: The final course grade will be based on:

1. Completing a “computational primer:” solving computationally for the deterministic steady state of the basic RBC model – 10% of final grade.

2. Computationally solving and simulating the basic RBC model, tabulating business cycle statistics and impulse responses (written as a complete, short paper) – 20% of final grade.

3. Two other projects to be assigned during the course, each of which will be computationally and/or analytically oriented (each written as a complete, short paper) – (total of 20% of final grade).

4. In-class presentation of a paper (from a designated set of papers) – 20% of final grade.

5. Assorted assignments, short writing pieces, quizzes, etc – 10% of final grade. Reference Texts: Some “all-purpose” macroeconomics and texts that are likely to be useful to have on your shelf/eshelf:

1. Frontiers of Business Cycle Research, 1995. Edited by Thomas F. Cooley. Princeton University Press.

2. Equilibrium Unemployment Theory, 2nd edition, 2000. By Christopher A. Pissarides. MIT Press.

3. Labor Markets and Business Cycles, 2010. By Robert Shimer. Princeton University Press.

4. Recursive Macroeconomic Theory, 3nd edition, 2012. By Lars Ljungqvist and Thomas J. Sargent. MIT Press.

5. Recursive Methods in Economic Dynamics, 1989. By Nancy L. Stokey and Robert E. Lucas, Jr., with Edward C. Prescott. Harvard University Press.

Monetary Theory I | © Sanjay K. Chugh 2

Objectives: There are three main objectives for the course. 1. First, the course will trace through some seminal branches of macroeconomic theory

over the past 30 years. Emphasis will be on business cycle modeling, which was the proximate cause of the revolution in macroeconomics 30 years ago, and macro-labor issues. We will trace these arcs of thought through to modern quantitative partial equilibrium and general equilibrium business cycle models, and identify/examine where some of the current research frontiers lie.

2. A second fundamental objective is to either get started on or continue becoming

comfortable with computational solutions of partial equilibrium and general equilibrium business cycle models. Modern macroeconomics can be computationally intensive. We will study basic tools that macroeconomists typically use to approximate and solve business cycle models. This means “rolling up your sleeves” and learning (if you do not know already) some basic programming and computing techniques. Our laboratory for developing computational techniques will first be the baseline RBC model, and then we will progress to models that introduce various departures from the baseline competitive RBC model.

3. Third, a necessary condition to be a successful economist (not just a successful

macroeconomist) is effective communication skills, both written and spoken. It is never too early to begin (or continue) developing such skills. I will insist that all assignments/projects be written as if they were small “papers,” with a clear motivation laid out at the outset, a clear presentation of the model(s) used, a clear description of the methodology employed, effective presentation of and discussion of results, and so on. The required in-class presentation of a paper (from among the set of papers I will designate as “student presentation”) also fosters this objective.

In all written submissions of papers, the following should be completely clear after the abstract and the first two paragraphs of your paper: the basic question your paper/project addresses; the big-picture answer(s) your paper provides; why this ought to be of interest to macroeconomists; and (related) how/along what dimensions your work advances the relevant field of knowledge. If, after reading the first two paragraphs of your submission, I judge that you have not clearly explained these basics, your paper will be returned to you ungraded for you to improve and resubmit.

Monetary Theory I | © Sanjay K. Chugh 3

Outline of Topics: The following is a list of topics and references. Due to time constraints, we will certainly not be able to cover all of these topics. Nevertheless, the topics we skip are, in my view, important ones in macroeconomics, so selected important readings and references for these are provided.

UNIT I: Arrow-Debreu General Equilibrium Theory and Introduction to Computational Methods and Tools

1. A (Brief and Partial) History of Macroeconomics and the Evolving Agenda

1. Prescott, Edward C. 2006. “Nobel Lecture: The Transformation of Macroeconomic

Policy and Research.” Journal of Political Economy, Vol. 114, pp. 203-235.

2. Kydland, Finn E. 2006. “Nobel Lecture: Quantitative Aggregate Economics.” American Economic Review, Vol. 96, pp. 1373-1383.

3. Diamond, Peter A. 2010. “Unemployment, Vacancies, Wages.” Nobel Lecture.

4. Mortensen, Dale T. 2010. “Markets with Search Friction and the DMP Model.” Nobel Lecture.

5. Pissarides, Christopher A. 2010. “Equilibrium in the Labour Market with Search

Frictions.” Nobel Lecture.

6. Lucas, Robert E. 1995. “Monetary Neutrality.” Nobel Lecture. 7. Solow, Robert M. 1987. “Growth Theory and After.” Nobel Lecture 8. Mankiw, N. Gregory. 2006. “The Macroeconomist as Scientist and Engineer.”

Journal of Economic Perspectives, Vol. 20, pp. 29-46.

9. Ohanian, Lee E. 2010. “The Economic Crisis from a Neoclassical Perspective.” Journal of Economic Perspectives, Vol. 24, Fall 2010, p. 45-66.

10. Blanchard, Olivier J. 2008. “The State of Macro.” NBER Working Paper No.

14259. 11. Akerlof, George A. 2007. “The Missing Motivation in Macroeconomics.” American

Economic Review, Vol. 97, pp. 5-36. 12. Chari, V.V. and Patrick J. Kehoe. 2006. “Modern Macroeconomics in Practice:

How Theory is Shaping Policy.” Journal of Economic Perspectives, Vol. 20, pp. 3-28.

Monetary Theory I | © Sanjay K. Chugh 4

13. Rebelo, Sergio T. 2005. “Real Business Cycle Models: Past, Present, and Future.” NBER Working Paper No. 11401.

14. Hall, Robert E. 2010. “Why Does the Economy Fall to Pieces After a Financial

Crisis?” Journal of Economic Perspectives, Vol. 24, Fall 2010, p. 3-20. 15. Woodford, Michael. 2010. “Financial Intermediation and Macroeconomic

Analysis.” Journal of Economic Perspectives, Vol. 24, Fall 2010, p. 21-44. 16. Fuster, Andreas, David Laibson, and Brock Mendel. 2010. “Natural Expectations

and Macroeconomic Fluctuations.” Journal of Economic Perspectives, Vol. 24, Fall 2010, p. 67-84.

17. Caballeo, Ricardo. 2010. “Macroeconomics after the Crisis: Time to Deal with the

Pretense-of-Knowledge Syndrome.” Journal of Economic Perspectives, Vol. 24, Fall 2010, p. 85-102.

2. Review of Dynamic Stochastic General Equilibrium (DSGE) Theory 18. King, Robert G. and Sergio T. Rebelo. 1999. “Resuscitating Real Business Cycles.”

In Handbook of Macroeconomics, Vol. 1B, edited by John B. Taylor and Michael Woodford.

19. Campbell, John Y. 1994. “Inspecting the Mechanism: An Analytical Approach to

the Stochastic Growth Model.” Journal of Monetary Economics, Vol. 33, pp. 463-506.

20. Ingram, Beth F., Narayana R. Kocherlakota, and N.E. Savin. 1994. “Explaining

Business Cycles: A Multiple-Shock Approach.” Journal of Monetary Economics, Vol. 34, pp. 415-428.

21. McGrattan, Ellen R. 2006. “Real Business Cycles.” Federal Reserve Bank of

Minneapolis Staff Report No. 370. 3. Review of / Basics of Dynamic Programming 22. Prescott, Edward C. and Rajnish Mehra. 1980. “Recursive Competitive Equilibrium:

The Case of Homogeneous Households.” Econometrica, Vol. 48, p. 1365-1379. 23. Ljungqvist and Sargent text, Chapter 1.4, Chapter 2.2, Chapter 3, 4, 5 24. Stokey, Lucas, and Prescott textbook

Monetary Theory I | © Sanjay K. Chugh 5

4. Basic Computational Methods and Calibration 25. King, Robert G., Charles I. Plosser, and Sergio T. Rebelo. 1988. “Production,

Growth, and Business Cycles I: The Basic Neoclassical Model.” Journal of Monetary Economics, Vol. 21, pp. 195-232.

26. King, Robert G., Charles I. Plosser, and Sergio T. Rebelo. 2002. “Production, Growth, and Business Cycles: Technical Appendix.” Computational Economics, Vol. 20, pp. 87-116.

27. Schmitt-Grohe, Stephanie and Martin Uribe. 2004. “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function.” Journal of Economic Dynamics and Control, Vol. 28, pp. 755-775.

28. Uhlig, Harald. 1999. “A Toolkit for Analyzing Nonlinear Dynamic Stochastic

Models Easily.” In Computational Methods for the Study of Dynamic Economies, edited by Ramon Marimon and Andrew Scott. Oxford Press.

29. Baxter, Marianne and Robert G. King. 1999. “Measuring Business Cycles:

Approximate Band-Pass Filters for Economic Time Series.” Review of Economics and Statistics, Vol. 81, p. 575-593.

30. Christiano, Lawrence J. and Terry J. Fitzgerald. 2003. “The Band Pass Filter.”

International Economic Review, Vol. 44, p. 435-465.

31. Kaldor, Nicholas. 1957. “A Model of Economic Growth.” Economic Journal, Vol. 67, p. 591-624.

32. Kuznets, Simon. 1973. “Modern Economic Growth: Findings and Reflections.”

American Economic Review, Vol. 63, p. 247-258.

33. Brock, William A. and Leonard J. Mirman. 1972. “Optimal Economic Growth and Uncertainty: The Discounted Case.” Journal of Economic Theory, Vol. 4, p. 479-513.

34. Hodrick, Robert J. and Edward C. Prescott. 1997. “Postwar U.S. Business Cycles:

An Empirical Investigation.” Journal of Money, Credit, and Banking, Vol. 29, pp. 1-16.

Monetary Theory I | © Sanjay K. Chugh 6

UNIT II: Macro-Labor 5. Macro-Labor I: Labor-Leisure Margin

35. Rogerson, Richard. 1988. “Indivisible Labor, Lotteries and Equilibrium.” Journal of

Monetary Economics, Vol. 21, pp. 3-16. 36. Hansen, Gary D. 1985. “Indivisible Labor and the Business Cycle.” Journal of

Monetary Economics, Vol. 16, pp. 309-327. 37. Mulligan, Casey B. 2001. “Aggregate Implications of Indivisible Labor.” B.E.

Journal of Macroeconomics: Advances in Macroeconomics, Vol. 1.

38. Cooley, Thomas F. and Gary D. Hansen. 1991. “The Welfare Costs of Moderate Inflation.” Journal of Money, Credit, and Banking, Vol. 23, pp. 483-503.

39. Cho, Jang-Ok and Thomas F. Cooley. 1994. “Employment and Hours Over the

Business Cycle.” Journal of Economic Dynamics and Control, Vol. 18, pp. 411-432. 40. Swanson, Eric. 2012. “Risk Aversion and the Labor Margin in Dynamic Equilibrium

Models.” American Economic Review, Vol. 102, p. 1663-1691.

41. Chetty, Raj, Adam Guren, Day Manoli, and Andrea Weber. “Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins.” American Economic Review Papers and Proceedings, May 2011 p. 471-5.

6. Macro-Labor II: Employment-Unemployment Margin 42. Pissarides, Christopher A. 2000. Equilibrium Unemployment Theory. MIT Press.

43. Shimer, Robert. 2010. Labor Markets and Business Cycles. Princeton University

Press.

44. Rogerson, Richard and Robert Shimer. 2011. “Search in Macroeconomic Models of the Labor Market.” Handbook of Labor Economics, Elsevier.

45. Rogerson, Richard, Robert Shimer, and Randall Wright. 2005. “Search-Theoretic

Models of the Labor Market: A Survey.” Journal of Economic Literature, Vol. 43, pp. 959-988.

46. Shimer, Robert. 2005. “The Cyclical Behavior of Equilibrium Unemployment and

Vacancies.” American Economic Review, Vol. 95, pp. 25-49.

Monetary Theory I | © Sanjay K. Chugh 7

47. Hall, Robert E. 2005. “Equilibrium Wage Stickiness.” American Economic Review, Vol. 95, pp. 50-65.

48. Hagedorn, Marcus and Iourii Manovskii. 2008. “The Cyclical Behavior of

Equilibrium Unemployment and Vacancies Revisited.” American Economic Review, Vol. 98, p. 1692-1706.

49. Hosios, Arthur J. 1990. “On the Efficiency of Matching and Related Models of

Search and Unemployment.” Review of Economic Studies, Vol. 57, p. 279-298.

50. Moen, Espen. 1997. “Competitive Search Equilibrium.” Journal of Political Economy, Vol. 105, pp. 385-411.

51. Stole, Lars A. and Jeffrey Zwiebel. 1996a. “Intra-firm Bargaining under Non-

Binding Contracts.” Review of Economic Studies, Vol. 63, p. 375-410.

52. Stole, Lars A. and Jeffrey Zwiebel. 1996b. “Organizational Design and Technology Choice Intra-firm Bargaining.” Review of Economic Studies, Vol. 63, p. 375-410.

53. Acemoglu, Daron and William B. Hawkins. 2014. “Search with Multi-Worker

Firms.” Theoretical Economics, Vol. 9, p. 583-628.

54. Shimer, Robert. 2012. “Reassessing the Ins and Outs of Unemployment.” Review of Economic Dynamics, Vol. 15, p. 127-148.

55. Shimer, Robert. 2012. “Wage Rigidity and Jobless Recoveries.” Journal of

Monetary Economics, Vol. 59, p. S65-S77.

56. Hall, Robert E. and Paul R. Milgrom. 2008. “The Limited Influence of Unemployment on the Wage Bargain.” American Economic Review, Vol. 98, p. 1653-1674.

57. Hall, Robert E. 2009. “Reconciling Cyclical Movements in the Marginal Value of

Time and the Marginal Product of Labor.” Journal of Political Economy, Vol. 117, p. 281-323.

58. Pissarides, Christopher A. 2009. “The Unemployment Volatility Puzzle: Is Wage

Stickiness the Answer?” Econometrica, Vol. 77, p. 1339-1369.

59. Andolfatto, David. 1996. “Business Cycles and Labor Market Search.” American Economic Review, Vol. 86, pp. 112-132.

60. Merz, Monika. 1995. “Search in the Labor Market and the Real Business Cycle.”

Journal of Monetary Economics, Vol. 36, pp. 269-300.

Monetary Theory I | © Sanjay K. Chugh 8

61. Mortensen, Dale and Christopher A. Pissarides. 1994. “Job Creation and Job Destruction in the Theory of Unemployment.” Review of Economic Studies, Vol. 61, p. 397-415.

62. denHaan, Wouter J., Garey Ramey, and Joel Watson. 2000. “Job Destruction and

Propagation of Shocks.” American Economic Review, Vol. 90, pp. 482-498. 63. Gertler, Mark and Antonella Trigari. 2009. “Unemployment Fluctuations with

Staggered Nash Bargaining.” Journal of Political Economy, Vol. 117, p. 38-86.

64. Davis, Steven J., R. Jason Faberman, and John C. Haltiwanger. 2013. “The Establishment-Level Behavior of Vacancies and Hiring.” Quarterly Journal of Economics, Vol. 127, p. 581-622.

65. Veracierto, Marcelo. 2008. “On the Cyclical Behavior of Employment,

Unemployment, and Labor Force Participation.” Journal of Monetary Economics, Vol. 55, pp. 1143-1157.

66. Alvarez, Fernando and Robert Shimer. 2011. “Search and Rest Unemployment.”

Econometrica, Vol. 79, pp. 75-122.

67. Ebrahimy, Ehsan and Robert Shimer. 2010. “Stock-Flow Matching.” Journal of Economic Theory, Vol. 145, pp. 1325-1353.

68. Lucas, Robert E. and Edward C. Prescott. 1974. “Equilibrium Search and

Unemployment.” Journal of Economic Theory, Vol. 7, p. 188-209.

69. Aguiar, Mark, Erik Hurst, and Loukas Karabarbounis. 2013. “Time Use During the Great Recession.” American Economic Review, Vol. 103, pp. 1664-1696.

70. Nakajima, Makoto. 2012. “Business Cycles in the Equilibrium Model of Labor

Market Search and Self-Insurance.” International Economic Review, Vol. 53, p. 399-431.

71. Krusell, Per, Toshihiko Mukoyama, and Aysegul Sahin. 2010. “Labour-Market

Matching with Precautionary Savings and Aggregate Fluctuations.” Review of Economic Studies, Vol. 77, p. 1477-1507.

72. Chugh, Sanjay K. and Christian Merkl. 2015. “Efficiency and Labor Market

Dynamics in a Model of Labor Selection.” International Economic Review. Forthcoming.

Monetary Theory I | © Sanjay K. Chugh 9

UNIT III: Product Markets

7. Product Markets 73. Diamond, Peter A. 1971. “A Model of Price Adjustment.” Journal of Economic

Theory, Vol. 3, p. 156-168.

74. Chamberlin, Edward. 1933. The Theory of Monopolistic Competition.

75. Robinson, Joan. 1933. The Economics of Imperfect Competition.

76. Dixit, Avinash K. and Joseph E. Stiglitz. 1977. “Monopolistic Competition and Optimum Product Diversity.” American Economic Review, Vol. 67, p. 297-308.

77. Klemperer, Paul. 1995. “Competition When Consumers Have Switching Costs: An

Overview with Applications to Industrial Organization, Macroeconomics, and International Trade.” Review of Economic Studies, Vol. 62, pp. 515-539.

78. Benassy, Jean-Pascal. 1996. “Taste for Variety and Optimum Production Patterns in Monopolistic Competition.” Economics Letters, Vol. 52, p. 41-47.

79. Leary, J. Peter. 2001. “Of Hype and Hyperbolas: Introducing the New Economic

Geography.” Journal of Economic Literature, Vol. XXXIX, p. 536-561.

80. Feenstra, Robert C. 2003. “A Homothetic Utility Function for Monopolistic Competition Models, Without Constant Price Elasticity.” Economics Letters, Vol. 78, p. 79-86.

81. [Student Presentation – October 27, 2015.] Comin, Diego and Mark Gertler. 2006.

“Medium-Term Business Cycles.” American Economic Review, Vol. 96, p. 523-551.

82. Bilbiie, Florin O., Fabio Ghironi, and Marc J. Melitz. 2012. “Endogenous Entry, Product Variety, and Business Cycles.” Journal of Political Economy, Vol. 120, p. 304-345.

83. [Student Presentation – October 29, 2015.] Saez, Emmanuel and Pascal Michaillet.

2015. “Aggregate Demand, Idle Time, and Unemployment.” Quarterly Journal of Economics, Vol. 130, p. 507-569.

84. Saez, Emmanuel and Pascal Michaillet. 2015. “An Economical Business-Cycle

Model.” Working Paper. 85. [Student Presentation – November 3, 2015.] Gourio, Francois and Leena Rudanko.

2014. “Customer Capital.” Review of Economic Studies, Vol. 81, p. 1102-1136.

Monetary Theory I | © Sanjay K. Chugh 10

UNIT IV: Optimal Fiscal Policy 8. Optimal Fiscal Policy: The Macro-Ramsey Approach 86. Ramsey, Frank. 1927. “A Contribution to the Theory of Taxation.” Economic

Journal, Vol. 37, pp. 47-61.

87. Stiglitz, Joseph E. 2014. “In Praise of Frank Ramsey’s Contribution to the Theory of Taxation.” NBER Working Paper 20530.

88. Lucas, Robert E. and Nancy L. Stokey. 1983. “Optimal Fiscal and Monetary Policy

in an Economy Without Capital.” Journal of Monetary Economics, Vol. 12, pp. 55-93.

89. Chamley, Christophe. 1986. “The Welfare Cost of Capital Income Taxation in a

Growing Economy.” Econometrica, Vol. 54, pp. 607-622.

90. Judd, Kenneth L. 1985. “Redistributive Taxation in a Simple Perfect Foresight Model.” Journal of Public Economics, Vol. 28, pp. 59-83.

91. Chari, V.V., Lawrence J. Christiano, and Patrick Kehoe. 1991. “Optimal Fiscal and

Monetary Policy: Some Recent Results.” Journal of Money, Credit, and Banking, Vol. 23, pp. 519-539.

92. Chari, V.V. and Patrick J. Kehoe. 1999. “Optimal Fiscal and Monetary Policy.” In

Handbook of Macroeconomics, Vol. 1C, edited by John B. Taylor and Michael Woodford.

93. Schmitt-Grohe, Stephanie and Martin Uribe. 2004. “Optimal Fiscal and Monetary

Policy Under Imperfect Competition.” Journal of Macroeconomics, Vol. 26, pp. 183-209.

94. Schmitt-Grohe, Stephanie and Martin Uribe. 2004. “Optimal Fiscal and Monetary

Policy Under Sticky Prices.” Journal of Economic Theory, Vol. 114, pp. 198-230. 95. Siu, Henry E. 2004. “Optimal Fiscal and Monetary Policy with Sticky Prices.”

Journal of Monetary Economics, Vol. 51, pp. 576-607. 96. Chugh, Sanjay K. 2006. “Optimal Fiscal and Monetary Policy with Sticky Wages

and Sticky Prices.” Review of Economic Dynamics, Vol. 9, pp. 683-714. 97. Chugh, Sanjay K. 2007. “Optimal Inflation Persistence: Ramsey Taxation with

Capital and Habits.” Journal of Monetary Economics, Vol. 54, pp. 1809-1836.

Monetary Theory I | © Sanjay K. Chugh 11

98. Arseneau, David M. and Sanjay K. Chugh. 2008. “Optimal Fiscal and Monetary Policy with Costly Wage Bargaining.” Journal of Monetary Economics, Vol. 55, p. 1401-1414.

99. Arseneau, David M. and Sanjay K. Chugh. 2012. “Tax Smoothing in Frictional Labor Markets.” Journal of Political Economy, Vol. 120, p. 926-985.

100. Chugh, Sanjay K. and Fabio Ghironi. 2015. “Optimal Fiscal Policy with

Endogenous Product Variety.” CEPR Discussion Paper Series No. 10674.

101. Arseneau, David M., Ryan Chahrour, Sanjay K. Chugh, and Alan Finkelstein-Shapiro. 2015. “Optimal Fiscal and Monetary Policy in Customer Markets.” Journal of Money, Credit, and Banking, Vol. 47, p. 617-672.

102. Arseneau, David M., Sanjay K. Chugh, and Andre Kurmann. 2008. “Optimal

Capital Taxation in an Economy with Capital Allocation Frictions.”

103. Aruoba, S. Boragan and Sanjay K. Chugh. 2010. “Optimal Fiscal and Monetary Policy when Money is Essential.” Journal of Economic Theory, Vol. 145, pp. 1618-1647.